Question

(-3+2iroot48)(-5-4iroot12)

Answer 1

For this case we must simplify the following expression:

`(-3 + 2i \sqrt {48}) (- 5-4i \sqrt {12})`

Rewriting:

`(-3 + 2i \sqrt {4 ^ 2 * 3}) (- 5-4i \sqrt {2 ^ 2 * 3}) =\\(-3 + 2 * 4i \sqrt {3}) (- 5-4 * 2i \sqrt {3}) =\\(-3 + 8i \sqrt {3}) (- 5-8i \sqrt {3}) =`

We apply distributive property:

`- * - = +\\- * + = -\\15 + 24i \sqrt {3} -40i \sqrt {3} - (8i \sqrt {3}) ^ 2 =\\15 + 24i \sqrt {3} -40i \sqrt {3} -64i ^ 2 * 3 =`

We have to
`i ^ 2 = -1`:

`15 + 24i \sqrt {3} -40i \sqrt {3} + 192 =`

Adding similar terms:

`207-16i \sqrt {3}`

Answer:

`207-16i \sqrt {3}`